Resultant force-couple system where resultant couple is 0

[Francis Hannah]

For the structure, find the distance from O (in direction OA) to the point where the resultant force-couple system of the forces shown should have a resultant couple of zero. Give answer in metres.

a=90 N, b=289 N, c=549 N

Clockwise negative, anticlockwise positive.

Moment at a = (1+2+2.5cos45)(90) = 429.099 Nm

Moment at b = -(2.5sin45)(298) = -510.885 Nm

Moment at c = -(1)(459) = -549 Nm

Hence, the resultant moment = -630.7856 Nm

Forces in the x-direction = 289 N

Forces in the y-direction = -459 N

Resultant force = 542.404 N.

Hence m = fd, so d = m/f ⇒ d = -630.7856/542.404 = -1.163.

Absolute value of d = 1.163m

However, the answer I got is somehow incorrect, and I have no idea where I've gone wrong!

What does it mean by a "resultant couple of zero"?

Thanks for helping :)

 

[J Hann]

You can do quick check by taking the torques about point A.
This should show you that there is net counter-clockwise torque.
Because of the large value of Fc, apparently the point of zero torque must lie between O and A.
Now, how would you find the net torque about a point say (A - x)?

 

[PhanthomJay]

You should first correct your typo for the moment at b...you used 298 instead of 289.

Otherwise , your determination of the resultant distance is the perpendicular distance from the line of action of the resultant force to O, but the problem asks specifically for the distance of the resultant force along the horizontal OA direction.

The 'resultant couple of zero' means that your resultant is just a force without a couple.

 

[Francis Hannah]

You should first correct your typo for the moment at b...you used 298 instead of 289.

Otherwise , your determination of the resultant distance is the perpendicular distance from the line of action of the resultant force to O, but the problem asks specifically for the distance of the resultant force along the horizontal OA direction.

The 'resultant couple of zero' means that your resultant is just a force without a couple.

If I have to find the distance along the horizontal, for m = f ⋅ d, instead of using the resultant force for f, should I use fy, the sum of forces along the y-axis?

 

[PhanthomJay]

If I have to find the distance along the horizontal, for m = f ⋅ d, instead of using the resultant force for f, should I use fy, the sum of forces along the y-axis?

Yes, that should do it.